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The notion of Kolmogorov complexity can be used to state and [[Proof of impossibility|prove impossibility]] results akin to [[Cantor's diagonal argument]], [[Gödel's incompleteness theorem]], and [[halting problem|Turing's halting problem]].
In particular, no program ''P'' computing a [[lower bound]] for each text's Kolmogorov complexity can return a value essentially larger than ''P''<nowiki>'</nowiki>s own length (see section {{slink||Chaitin's incompleteness theorem}}); hence no single program can compute the exact Kolmogorov complexity for infinitely many texts. Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. While Kolmogorov complexity is uncomputable, various approaches have been proposed and reviewed.<ref name="zenil20202">{{cite journal |last1=Zenil |first1=Hector |year=2020 |title=A Review of Methods for Estimating Algorithmic Complexity: Options, Challenges, and New Directions
==Definition==
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